 | John Playfair - 1819 - 354 sider
...is equal to the remainder (3. Ax.) BG : But it has been shewn that BC is equal to BG ; wherefore AL and BC are each of them equal to BG ; and things that...line AL has been drawn equal to the given straight line1 BC. Which was to be done. PROP. III. PROB. From the greater of two given straight lines to cut... | |
 | Charles Tayler - 1824 - 350 sider
...will be as follows ; viz. From the first equation, x=.°~ -^ From the second x ~ -~ ^ . a' Now since things that are equal to the same are equal to one another, these two values of x are equal ; and we have therefore this new equation ; c— by __d— b'y, ~a~... | |
 | Peter Nicholson - 1825 - 1046 sider
...is equal to the remainder (3 Ax.) BG : But it has oeen shown, that BC is equal to BG ; wherefore AL and BC are each of them equal to BG ; and things that...AL is equal to BC. Wherefore from the given point À a straight line AL has been drawn equal to the given straight Une BC. • Which was to be done.... | |
 | Euclid, John Playfair - 1826 - 326 sider
...remainder (3. Ax.) BG : But it has been shewn that BC is equal to BG : wherefore AL and BC are eaeh B of them equal to BG ; and things that are equal to...has been drawn equal to the given straight line BC. Whieh was to be done. PROP. III. PROB. From the greater of two given straight lines to eut off a part... | |
 | Euclides - 1826 - 226 sider
...EBA, ABC. But it was shown that the angles CBE, EBD, are equal to the same three, and things which are equal to the same are equal to one another; therefore the angles CBE, EBD, are equal to DBA, ABC; but CBE, EBD, are two right angles; therefore the angles DBA,... | |
 | Euclid - 1826 - 234 sider
...EBA, ABC. But it was shown that the angles CBE, BBD, are equal to the same three, and things which are equal to the same are equal to one another; therefore the angles CBE, EBD, are equal to DBA, ABC; but CBE, EBD, are two right angles ; therefore the angles DBA,... | |
 | Robert Simson - 1827 - 546 sider
...1 Ax. '2.1. ' 3 Post. t 15 Def. t Constr. •1Ax. that BC is equal to BG ; wherefore AL nnd BC nre each of them equal to BG : and things that are equal to the same thing are equal-)- to one another; therefore the straight line AL is equal to BC. Wherefore from the... | |
 | John Playfair - 1832 - 358 sider
...AL is equal to the remainder (3. Ax.) BG: But it has been shewn that BC is equal to BG; wherefore AL and BC are each of them equal to BG; and things that are equal to the same are equal to one another;thereforethestraight line AL is equal to BC. Wherefore, from the given point A, a straight... | |
 | Alexander Campbell, Charles Louis Loos - 1832 - 656 sider
...effect of the Spirit mean the same thing, for water means the Spirit and the effect of the Spirit: and things that are equal to the same are equal to one another! What does not the phrase ''born of water" mean? It is equal to born ofjire, born of like as of Jire,... | |
 | 1835 - 518 sider
...argument to prove, that a dog runs on four feet : and so a cat is like a fox, and a dog is like a fox, and things that are equal to the same are equal to one another ; and so a cat is a dog, and a dog is a cat ; and so, your Honours, I trust I have established my defence,... | |
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DL is equal to DG, and DA, DB, parts of them, are equal ; therefore the remainder AL is equal to the remainder (3. Ax.) BG : But it has been shewn that BC is equal to BG ; wherefore AL and BC are each of them equal to BG ; and things that are equal to... 
